Almost sure stability and stabilization of discrete-time stochastic systems

As is well known, noise may play a stabilizing or destabilizing role in continuous-time systems. But, for analysis and design of discrete-time systems, noise is treated as disturbance in the literature. This paper studies almost sure stability of general n-dimensional nonlinear time-varying discrete-time stochastic systems and presents a criterion based on a numerical result derived from Higham (2001), which exploits the stabilizing role of noise in discrete-time systems. As an application of the established results, this paper proposes a novel controller design method for almost sure stabilization of linear discrete-time stochastic systems. The effectiveness of the proposed design method is verified with an example (an aircraft model subject to state-dependent noise), to which the existing results do not apply.